Homework Help is Here – Start Your Trial Now!
Math
Calculus
Let à = − 3ỉ − 2j + 2k. Find ||ā||.

Let à = − 3ỉ − 2j + 2k. Find ||ā||.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question

1.1.2

**Problem Statement: Vector Magnitude** Let \(\vec{a} = -3\vec{i} - 2\vec{j} + 2\vec{k}\). Find \(\|\vec{a}\|\). --- **Solution:** The magnitude of a vector \(\vec{a} = a_1\vec{i} + a_2\vec{j} + a_3\vec{k}\) is given by the formula: \[ \|\vec{a}\| = \sqrt{a_1^2 + a_2^2 + a_3^2} \] For \(\vec{a} = -3\vec{i} - 2\vec{j} + 2\vec{k}\): - \(a_1 = -3\) - \(a_2 = -2\) - \(a_3 = 2\) Substitute these values into the formula: \[ \|\vec{a}\| = \sqrt{(-3)^2 + (-2)^2 + (2)^2} \] \[ \|\vec{a}\| = \sqrt{9 + 4 + 4} \] \[ \|\vec{a}\| = \sqrt{17} \] Therefore, the magnitude of \(\vec{a}\) is \(\sqrt{17}\). --- This exercise helps in understanding how to calculate the magnitude of a vector in three-dimensional space using its components.
Transcribed Image Text:**Problem Statement: Vector Magnitude** Let \(\vec{a} = -3\vec{i} - 2\vec{j} + 2\vec{k}\). Find \(\|\vec{a}\|\). --- **Solution:** The magnitude of a vector \(\vec{a} = a_1\vec{i} + a_2\vec{j} + a_3\vec{k}\) is given by the formula: \[ \|\vec{a}\| = \sqrt{a_1^2 + a_2^2 + a_3^2} \] For \(\vec{a} = -3\vec{i} - 2\vec{j} + 2\vec{k}\): - \(a_1 = -3\) - \(a_2 = -2\) - \(a_3 = 2\) Substitute these values into the formula: \[ \|\vec{a}\| = \sqrt{(-3)^2 + (-2)^2 + (2)^2} \] \[ \|\vec{a}\| = \sqrt{9 + 4 + 4} \] \[ \|\vec{a}\| = \sqrt{17} \] Therefore, the magnitude of \(\vec{a}\) is \(\sqrt{17}\). --- This exercise helps in understanding how to calculate the magnitude of a vector in three-dimensional space using its components.
Expert Solution
Step 1

Find the square root of the sum of the squares of the coefficients of each unit vector.

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS